On first and second order optimality conditions for abs-Normal NLP. (1st December 2020)

• Record Type: Journal Article
• Authors: Hegerhorst-Schultchen, L. C.; Steinbach, M. C.
• Is Part Of: Optimization. Volume 69:Number 12(2020)
• Page Start: 2629
• Page End: 2656
• Publication Date: 2020-12-01
• Subjects: Nonsmooth NLP -- abs-normal form -- linear independence kink qualification -- first and second order necessary and sufficient conditions; 49J52 -- 90C30 -- 90C46; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1626386
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : Structured nonsmoothness is widely present in practical optimization. A particularly attractive class of nonsmooth problems, both from a theoretical and from an algorithmic perspective, are optimization problems in so-called abs-normal form as developed by Griewank and Walther. Here we generalize their theory for the unconstrained case to nonsmooth NLPs with equality and inequality constraints in abs-normal form, obtaining similar necessary and sufficient conditions of first and second order that are directly based on classical Karush-Kuhn-Tucker (KKT) theory for smooth NLPs. Several small examples illustrate the theoretical results. We also give some brief remarks on the intimate relationship of abs-normal NLPs with MPECs.